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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Minimal Logics in the 2020's: A Meteoric Rise
Date: Fri, 5 Jul 2024 15:12:54 -0500
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On 7/5/2024 2:54 PM, Richard Damon wrote:
> On 7/5/24 1:38 PM, olcott wrote:
>> On 7/5/2024 11:23 AM, Richard Damon wrote:
>>> On 7/4/24 11:19 PM, olcott wrote:
>>>> On 7/4/2024 10:00 PM, Richard Damon wrote:
>>>>> On 7/4/24 10:38 PM, olcott wrote:
>>>>>> On 7/4/2024 8:58 PM, Mild Shock wrote:
>>>>>>>
>>>>>>> When red means blue, and yellow means
>>>>>>> green, then black is white. Thanks for your hint!
>>>>>>>
>>>>>>> If my Grandmother had wheels she would have been a bike
>>>>>>> https://www.youtube.com/watch?v=OplyHCIBmfE
>>>>>>>
>>>>>>
>>>>>> *Here is the same thing more clearly*
>>>>>> Every expression of language that is {true on the basis of
>>>>>> its verbal meaning} is only made true by a sequence of truth
>>>>>> preserving operations to this {verbal meaning}.
>>>>>>
>>>>>> The only way that we know that puppies are not fifteen
>>>>>> story office buildings is that the accurate verbal model
>>>>>> of the actual world tells use so.
>>>>>
>>>>> But, even if we can't find that sequence of truth perserving 
>>>>> operations, but one exists (which might be infinite) makes the 
>>>>> statement true, but not known.
>>>>>
>>>>> This is one of your confusions, You confuse a statment being True, 
>>>>> with the statement being KNOWN to be True.
>>>>>
>>>>> There are a number of great problems and conjectures that seem to 
>>>>> be true, but we can not prove them. They MUST be either True or 
>>>>> False, as by their nature, there is no middle ground (something 
>>>>> either exsits or it doesn't, or the count of something is either 
>>>>> finite or infinite).
>>>>>
>>>>> The ACTUAL TRUTH  (or falsehood) of such a statement is thus firmly 
>>>>> established by the system in which the conjeture is embedded, even 
>>>>> if our knowledge of the value of the truth of the statement is not 
>>>>> known, or possible even knowable.
>>>>>
>>>>> The concept of "incompleteness" for a logical system is a 
>>>>> recognition that the system has grown powerful enough that there 
>>>>> exist some truths in the system that no finite proof of those 
>>>>> statements exist, and only infinite chains of inference in the 
>>>>> system can establish it.
>>>>>
>>>>> Mathematics is one source for these sorts of truths, as the 
>>>>> possiblity of problems having NO number that satisfy them, or an 
>>>>> infinite number that satisfy them show paths that can use in 
>>>>> infinite number of steps to prove them, and might only be provable 
>>>>> if some "inductive" shortcut can be found.
>>>>>
>>>>
>>>> Yet my system screens out pathological expressions that
>>>> are incorrectly determined to be incompleteness of the
>>>> formal system. When we do that then True(L,x) can be defined
>>>> for every expression not requiring an infinite sequence
>>>> of steps. True(L,x) or True(L,~x) or not a truth bearer in L.
>>>
>>> No, it dies in self-inconsistency.
>>>
>>> Note "Every expression BUT ..."  isn't "Every expresion ."
>>>
>>
>> Every expression such that neither X nor ~X is provable in L
>> is simply not a truth bearer in L. This does correctly reject
>> self-contradictory expressions that wold otherwise be interpreted
>> as the incompleteness of L.
> 
> FALSE STATEMENT.
> 

Can't be false it is stipulated.

> Some statements are true due to an infinite number of steps to ther 
> truth-makers of the system.
> 

Already covered that.

> You will lead your logic system into contradictions by your definition 
> (or you just need to treat it as a worthless phrase that doesn't 
> actually tell you anything, particually what you call non-truth-bearers, 
> which might actuall be statement that are true or false).
> 

Not at all. Such a system does detect and reject self-contradictory
expressions thus does not use this as any basis for incompleteness.

>>
>> This works correctly for every element of the accurate verbal
>> model of the actual world. Since we can see that things like
>> the Goldbach conjecture can be proven *OR REFUTED* in an infinite
>> sequence then an algorithm can see this too. For everything
>> else it is an infallibly correct system of reasoning.
>>
> 
> So, you ADMIT that you definition doesn't work for some statements, and 
> thus is not correct.
> 

It detects expressions that require infinite steps as out
of scope and correctly determines all of the rest.

> Note, the algorithm can not tell wether the statement like to Goldback 
> conjecture is true or not, or even if it takes an infinite number of 
> steps to come to that answer. Thus, you statement is just a FALSEHOOD.
> 
Not at all. Because it is dead obvious to humans that Goldbach
can be proved or refuted in an infinite number of steps an
algorithm can see this too.

> You just don't understand logic well enough to understand that can't 
> have definitions that just don't work as the basis of a system.
> 
> By your definition, the Goldbach conjecture must currently be consider a 
> non-truth-bearer, but we KNOW that it must be either true or false, we 

It would be construed as out-of-scope.
Whether or not there was evidence of:
(a) Election fraud that could have possibly changed
the outcome of the 2020 presidential election or
(b) Very harmful climate change caused by humans
would be in scope.

> just don't know which, so you definition of a truth-bearer is just a lie.
> 
> What you are defining are KNOWLEDGE bearers, statements that there truth 
> can be known. 

The key problem that it solves is that it makes True(L,x)
computable for all of the most important things that really
matter.

You are essentially saying that
A cure for cancer is totally useless because it only cures
99.99% of cancers.

> But we can't even know if the Goldbach conjecture is a 
> knowledge-bearer or not. If it turns out to be false, then that fact is 
> knowable, but not yet known (since showing the number, as a simple 
> finite proof that no pair of primes below it sum to it make it prove 
> false), but if it is true, there might be a proof, or there might not be.
> 
> So even Knowledge-Bearers as a concept is has limited use. Knowledge, 
> that which we currently know, is a valid concept, and one that admits 
> things can be added to it.
> 
> And Truth-Bearers, with the allowance of infinite chains to establish 
> the truth (or falseness) of the statement can be useful, though we do 
> need to admit we don't know, and perhaps CAN'T know that truth value, 
> and need to allow for some statements that we don't yet have the ability 
> to know if they are truth-bearers or not.
> 
> But your definition of truth-bearers is just worthless for most logic 
> systems, claiming to be about truth but actually being about knowledge 
> isn't a good definition, and just shows your fundamental 
> misunderstanding about what is actually truth and how it differs from 
> knowledge.
> 
>>
>>> So, your logic only works in systems small enough to be somewhat akin 
>>> to toys. Those that are limited enough not to be able to cause the 
>>> problems, which means it excludes most systems that support math.
>>>
>>>>
>>>>>>
>>>>>>> olcott schrieb:
>>>>>>>> When provable means true and false means unprovable
>>>>>>>> then (Γ ⊢ X) means X is true in Γ.
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